Efficient pseudorandom functions from the decisional linear assumption and weaker variants
- 9 November 2009
- conference paper
- conference paper
- Published by Association for Computing Machinery (ACM)
- Vol. 2009, 112-120
- https://doi.org/10.1145/1653662.1653677
Abstract
In this paper, we generalize Naor and Reingold's construction of pseudorandom functions under the DDH Assumption [22] to yield a construction of pseudorandom functions under the decisional k-Linear Assumption, for each k › 1. The decisional Linear Assumption was first introduced by Boneh, Boyen, and Shacham in [5] as an alternative assumption for settings where the DDH problem is easy, such as bilinear groups. Shacham [25] and Hofheinz and Kiltz [16] independently introduced the generalized decisional k-Linear Assumptions and showed that the decisional (k+1)-Linear problem is hard for generic groups even when the decisional k-Linear problem is easy. It is thus desirable to have constructions of cryptographic primitives based on the decisional k-Linear Assumption instead of DDH. Not surprisingly, one must pay a small price for added security: as k increases, our constructed functions become slightly less efficient to compute and the key size increases (quadratically in k).Keywords
This publication has 13 references indexed in Scilit:
- How to Break MD5 and Other Hash FunctionsLecture Notes in Computer Science, 2005
- Appraising two decades of distributed computing theory researchDistributed Computing, 2003
- New Paradigms for Digital Signatures and Message Authentication Based on Non-Interactive Zero Knowledge ProofsPublished by Springer Science and Business Media LLC ,2001
- A Pseudorandom Generator from any One-way FunctionSIAM Journal on Computing, 1999
- Natural ProofsJournal of Computer and System Sciences, 1997
- Publicly Verifiable Secret SharingLecture Notes in Computer Science, 1996
- Reducing elliptic curve logarithms to logarithms in a finite fieldIEEE Transactions on Information Theory, 1993
- How to construct random functionsJournal of the ACM, 1986
- A theory of the learnableCommunications of the ACM, 1984
- New directions in cryptographyIEEE Transactions on Information Theory, 1976